{"abstract":"The decoded time state disagrees with the explicit regression oracle for inverse.","category":"Time representation","checks":11,"contract":"Two increasing device/reference calibration pairs define a positive exact affine clock mapping. Return rational slope/intercept, mapped device reading, signed observation-minus-prediction residual, inverse-mapped observed reference, and extrapolation direction (-1 before support, 0 within including anchors, 1 after). Fractions serialize canonically as strings.","contract_signature":"r","evaluation_group":"s3-time-affine_clock_calibration","failed_approach":"The partial correction still substitutes (r['observed'] + intercept) * reciprocal at the same fault site.","family":"s3-time_representation-affine-clock-calibration-inverse","id":"FA-17576","implementations":{"attempt":{"sha256":"c28edcf04a83453a27a5cf3b52d09c2fb12a44014ae889d0c906bd3b22372b14","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(r):\n    device_span = r['d1'] - r['d0']\n    reference_span = r['t1'] - r['t0']\n    slope = Fraction(reference_span, device_span)\n    reciprocal = 1 / slope\n    intercept = r['t0'] - slope * r['d0']\n    mapped = slope * r['reading'] + intercept\n    residual = r['observed'] - mapped\n    inverse = (r['observed'] + intercept) * reciprocal\n    fraction = Fraction(r['reading'] - r['d0'], device_span)\n    direction = -1 if fraction < 0 else (1 if fraction > 1 else 0)\n    return [str(slope),str(intercept),str(mapped),str(residual),str(inverse),direction]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1', solve({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 14}), ['3/2', '7', '13', '1', '14/3', 0])\ncheck('fixture 2', solve({'d0': -4, 'd1': 4, 't0': -10, 't1': 6, 'reading': -6, 'observed': -13}), ['2', '-2', '-14', '1', '-11/2', -1])\ncheck('fixture 3', solve({'d0': 1, 'd1': 5, 't0': 2, 't1': 4, 'reading': 8, 'observed': 5}), ['1/2', '3/2', '11/2', '-1/2', '7', 1])\ncheck('fixture 4', solve({'d0': 0, 'd1': 10, 't0': 5, 't1': 25, 'reading': 0, 'observed': 5}), ['2', '5', '5', '0', '0', 0])\ncheck('fixture 5', solve({'d0': 2, 'd1': 8, 't0': -3, 't1': 0, 'reading': 8, 'observed': 1}), ['1/2', '-4', '0', '1', '10', 0])\ncheck('fixture 6', solve({'d0': -8, 'd1': -2, 't0': 2, 't1': 14, 'reading': -5, 'observed': 7}), ['2', '18', '8', '-1', '-11/2', 0])\ncheck('fixture 7', solve({'d0': 4, 'd1': 10, 't0': 30, 't1': 39, 'reading': 10, 'observed': 40}), ['3/2', '24', '39', '1', '32/3', 0])\ncheck('fixture 8', solve({'d0': 2, 'd1': 5, 't0': 1, 't1': 2, 'reading': 3, 'observed': 1}), ['1/3', '1/3', '4/3', '-1/3', '2', 0])\ncheck('fixture 9', solve({'d0': 3, 'd1': 9, 't0': 4, 't1': 16, 'reading': 3, 'observed': 4}), ['2', '-2', '4', '0', '3', 0])\ncheck('fixture 10', solve({'d0': 1, 'd1': 2, 't0': 1, 't1': 3, 'reading': 2, 'observed': 3}), ['2', '-1', '3', '0', '2', 0])\nvariant = [({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 15}, ['3/2', '7', '13', '2', '16/3', 0]), ({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 16}, ['3/2', '7', '13', '3', '6', 0]), ({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 17}, ['3/2', '7', '13', '4', '20/3', 0]), ({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 18}, ['3/2', '7', '13', '5', '22/3', 0]), ({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 19}, ['3/2', '7', '13', '6', '8', 0])]\ncheck(\"variant capture\", solve(variant[N-1][0]), variant[N-1][1])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"e9d7e6109faed16b8db47880cf56d37dcc1007c5289b013ef417b29f4dee3c0a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(r):\n    device_span = r['d1'] - r['d0']\n    reference_span = r['t1'] - r['t0']\n    slope = Fraction(reference_span, device_span)\n    reciprocal = 1 / slope\n    intercept = r['t0'] - slope * r['d0']\n    mapped = slope * r['reading'] + intercept\n    residual = r['observed'] - mapped\n    inverse = r['observed'] * reciprocal - intercept\n    fraction = Fraction(r['reading'] - r['d0'], device_span)\n    direction = -1 if fraction < 0 else (1 if fraction > 1 else 0)\n    return [str(slope),str(intercept),str(mapped),str(residual),str(inverse),direction]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1', solve({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 14}), ['3/2', '7', '13', '1', '14/3', 0])\ncheck('fixture 2', solve({'d0': -4, 'd1': 4, 't0': -10, 't1': 6, 'reading': -6, 'observed': -13}), ['2', '-2', '-14', '1', '-11/2', -1])\ncheck('fixture 3', solve({'d0': 1, 'd1': 5, 't0': 2, 't1': 4, 'reading': 8, 'observed': 5}), ['1/2', '3/2', '11/2', '-1/2', '7', 1])\ncheck('fixture 4', solve({'d0': 0, 'd1': 10, 't0': 5, 't1': 25, 'reading': 0, 'observed': 5}), ['2', '5', '5', '0', '0', 0])\ncheck('fixture 5', solve({'d0': 2, 'd1': 8, 't0': -3, 't1': 0, 'reading': 8, 'observed': 1}), ['1/2', '-4', '0', '1', '10', 0])\ncheck('fixture 6', solve({'d0': -8, 'd1': -2, 't0': 2, 't1': 14, 'reading': -5, 'observed': 7}), ['2', '18', '8', '-1', '-11/2', 0])\ncheck('fixture 7', solve({'d0': 4, 'd1': 10, 't0': 30, 't1': 39, 'reading': 10, 'observed': 40}), ['3/2', '24', '39', '1', '32/3', 0])\ncheck('fixture 8', solve({'d0': 2, 'd1': 5, 't0': 1, 't1': 2, 'reading': 3, 'observed': 1}), ['1/3', '1/3', '4/3', '-1/3', '2', 0])\ncheck('fixture 9', solve({'d0': 3, 'd1': 9, 't0': 4, 't1': 16, 'reading': 3, 'observed': 4}), ['2', '-2', '4', '0', '3', 0])\ncheck('fixture 10', solve({'d0': 1, 'd1': 2, 't0': 1, 't1': 3, 'reading': 2, 'observed': 3}), ['2', '-1', '3', '0', '2', 0])\nvariant = [({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 15}, ['3/2', '7', '13', '2', '16/3', 0]), ({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 16}, ['3/2', '7', '13', '3', '6', 0]), ({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 17}, ['3/2', '7', '13', '4', '20/3', 0]), ({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 18}, ['3/2', '7', '13', '5', '22/3', 0]), ({'d0': 2, 'd1': 6, 't0': 10, 't1': 16, 'reading': 4, 'observed': 19}, ['3/2', '7', '13', '6', '8', 0])]\ncheck(\"variant capture\", solve(variant[N-1][0]), variant[N-1][1])\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Deterministic integer reference model with stipulated units and policies; not a complete clock, wire standard or platform implementation. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"s3-time_representation-affine-clock-calibration-inverse","generated_at":"2026-09-29T14:39:48.307007+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Clock transfer and timestamp consumers require preserved coordinate, phase, validity and elapsed-time semantics.","root_cause":"Inverse mapping removes bias after rate conversion.","sha256":"81786c37c313ff1f312f3b8ee9657f118e26a928bf01084f195a59441e8d37b5","title":"Inverse mapping removes bias after rate conversion · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":55.759,"exit_code":1,"observations":[{"actual":["3/2","7","13","1","14",0],"check":"fixture 1","expected":["3/2","7","13","1","14/3",0],"passed":false},{"actual":["2","-2","-14","1","-15/2",-1],"check":"fixture 2","expected":["2","-2","-14","1","-11/2",-1],"passed":false},{"actual":["1/2","3/2","11/2","-1/2","13",1],"check":"fixture 3","expected":["1/2","3/2","11/2","-1/2","7",1],"passed":false},{"actual":["2","5","5","0","5",0],"check":"fixture 4","expected":["2","5","5","0","0",0],"passed":false},{"actual":["1/2","-4","0","1","-6",0],"check":"fixture 5","expected":["1/2","-4","0","1","10",0],"passed":false},{"actual":["2","18","8","-1","25/2",0],"check":"fixture 6","expected":["2","18","8","-1","-11/2",0],"passed":false},{"actual":["3/2","24","39","1","128/3",0],"check":"fixture 7","expected":["3/2","24","39","1","32/3",0],"passed":false},{"actual":["1/3","1/3","4/3","-1/3","4",0],"check":"fixture 8","expected":["1/3","1/3","4/3","-1/3","2",0],"passed":false},{"actual":["2","-2","4","0","1",0],"check":"fixture 9","expected":["2","-2","4","0","3",0],"passed":false},{"actual":["2","-1","3","0","1",0],"check":"fixture 10","expected":["2","-1","3","0","2",0],"passed":false},{"actual":["3/2","7","13","2","44/3",0],"check":"variant capture","expected":["3/2","7","13","2","16/3",0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1\", \"actual\": [\"3/2\", \"7\", \"13\", \"1\", \"14\", 0], \"expected\": [\"3/2\", \"7\", \"13\", \"1\", \"14/3\", 0], \"passed\": false}, {\"check\": \"fixture 2\", \"actual\": [\"2\", \"-2\", \"-14\", \"1\", \"-15/2\", -1], \"expected\": [\"2\", \"-2\", \"-14\", \"1\", \"-11/2\", -1], \"passed\": false}, {\"check\": \"fixture 3\", \"actual\": [\"1/2\", \"3/2\", \"11/2\", \"-1/2\", \"13\", 1], \"expected\": [\"1/2\", \"3/2\", \"11/2\", \"-1/2\", \"7\", 1], \"passed\": false}, {\"check\": \"fixture 4\", \"actual\": [\"2\", \"5\", \"5\", \"0\", \"5\", 0], \"expected\": [\"2\", \"5\", \"5\", \"0\", \"0\", 0], \"passed\": false}, {\"check\": \"fixture 5\", \"actual\": [\"1/2\", \"-4\", \"0\", \"1\", \"-6\", 0], \"expected\": [\"1/2\", \"-4\", \"0\", \"1\", \"10\", 0], \"passed\": false}, {\"check\": \"fixture 6\", \"actual\": [\"2\", \"18\", \"8\", \"-1\", \"25/2\", 0], \"expected\": [\"2\", \"18\", \"8\", \"-1\", \"-11/2\", 0], \"passed\": false}, {\"check\": \"fixture 7\", \"actual\": [\"3/2\", \"24\", \"39\", \"1\", \"128/3\", 0], \"expected\": [\"3/2\", \"24\", \"39\", \"1\", \"32/3\", 0], \"passed\": false}, {\"check\": \"fixture 8\", \"actual\": [\"1/3\", \"1/3\", \"4/3\", \"-1/3\", \"4\", 0], \"expected\": [\"1/3\", \"1/3\", \"4/3\", \"-1/3\", \"2\", 0], \"passed\": false}, {\"check\": \"fixture 9\", \"actual\": [\"2\", \"-2\", \"4\", \"0\", \"1\", 0], \"expected\": [\"2\", \"-2\", \"4\", \"0\", \"3\", 0], \"passed\": false}, {\"check\": \"fixture 10\", \"actual\": [\"2\", \"-1\", \"3\", \"0\", \"1\", 0], \"expected\": [\"2\", \"-1\", \"3\", \"0\", \"2\", 0], \"passed\": false}, {\"check\": \"variant capture\", \"actual\": [\"3/2\", \"7\", \"13\", \"2\", \"44/3\", 0], \"expected\": [\"3/2\", \"7\", \"13\", \"2\", \"16/3\", 0], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":54.45,"exit_code":1,"observations":[{"actual":["3/2","7","13","1","7/3",0],"check":"fixture 1","expected":["3/2","7","13","1","14/3",0],"passed":false},{"actual":["2","-2","-14","1","-9/2",-1],"check":"fixture 2","expected":["2","-2","-14","1","-11/2",-1],"passed":false},{"actual":["1/2","3/2","11/2","-1/2","17/2",1],"check":"fixture 3","expected":["1/2","3/2","11/2","-1/2","7",1],"passed":false},{"actual":["2","5","5","0","-5/2",0],"check":"fixture 4","expected":["2","5","5","0","0",0],"passed":false},{"actual":["1/2","-4","0","1","6",0],"check":"fixture 5","expected":["1/2","-4","0","1","10",0],"passed":false},{"actual":["2","18","8","-1","-29/2",0],"check":"fixture 6","expected":["2","18","8","-1","-11/2",0],"passed":false},{"actual":["3/2","24","39","1","8/3",0],"check":"fixture 7","expected":["3/2","24","39","1","32/3",0],"passed":false},{"actual":["1/3","1/3","4/3","-1/3","8/3",0],"check":"fixture 8","expected":["1/3","1/3","4/3","-1/3","2",0],"passed":false},{"actual":["2","-2","4","0","4",0],"check":"fixture 9","expected":["2","-2","4","0","3",0],"passed":false},{"actual":["2","-1","3","0","5/2",0],"check":"fixture 10","expected":["2","-1","3","0","2",0],"passed":false},{"actual":["3/2","7","13","2","3",0],"check":"variant capture","expected":["3/2","7","13","2","16/3",0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1\", \"actual\": [\"3/2\", \"7\", \"13\", \"1\", \"7/3\", 0], \"expected\": [\"3/2\", \"7\", \"13\", \"1\", \"14/3\", 0], \"passed\": false}, {\"check\": \"fixture 2\", \"actual\": [\"2\", \"-2\", \"-14\", \"1\", \"-9/2\", -1], \"expected\": [\"2\", \"-2\", \"-14\", \"1\", \"-11/2\", -1], \"passed\": false}, {\"check\": \"fixture 3\", \"actual\": [\"1/2\", \"3/2\", \"11/2\", \"-1/2\", \"17/2\", 1], \"expected\": [\"1/2\", \"3/2\", \"11/2\", \"-1/2\", \"7\", 1], \"passed\": false}, {\"check\": \"fixture 4\", \"actual\": [\"2\", \"5\", \"5\", \"0\", \"-5/2\", 0], \"expected\": [\"2\", \"5\", \"5\", \"0\", \"0\", 0], \"passed\": false}, {\"check\": \"fixture 5\", \"actual\": [\"1/2\", \"-4\", \"0\", \"1\", \"6\", 0], \"expected\": [\"1/2\", \"-4\", \"0\", \"1\", \"10\", 0], \"passed\": false}, {\"check\": \"fixture 6\", \"actual\": [\"2\", \"18\", \"8\", \"-1\", \"-29/2\", 0], \"expected\": [\"2\", \"18\", \"8\", \"-1\", \"-11/2\", 0], \"passed\": false}, {\"check\": \"fixture 7\", \"actual\": [\"3/2\", \"24\", \"39\", \"1\", \"8/3\", 0], \"expected\": [\"3/2\", \"24\", \"39\", \"1\", \"32/3\", 0], \"passed\": false}, {\"check\": \"fixture 8\", \"actual\": [\"1/3\", \"1/3\", \"4/3\", \"-1/3\", \"8/3\", 0], \"expected\": [\"1/3\", \"1/3\", \"4/3\", \"-1/3\", \"2\", 0], \"passed\": false}, {\"check\": \"fixture 9\", \"actual\": [\"2\", \"-2\", \"4\", \"0\", \"4\", 0], \"expected\": [\"2\", \"-2\", \"4\", \"0\", \"3\", 0], \"passed\": false}, {\"check\": \"fixture 10\", \"actual\": [\"2\", \"-1\", \"3\", \"0\", \"5/2\", 0], \"expected\": [\"2\", \"-1\", \"3\", \"0\", \"2\", 0], \"passed\": false}, {\"check\": \"variant capture\", \"actual\": [\"3/2\", \"7\", \"13\", \"2\", \"3\", 0], \"expected\": [\"3/2\", \"7\", \"13\", \"2\", \"16/3\", 0], \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}